Dope Sheet Key Automation/Effects/Preset
I've written this script to shift all the keyframes at once.

Select the objects
Open the script in the Text Edit
Set the amount of frames, eg: step(10)
Run script (Alt + P)


import bpy

def shift(step):
    interval = 0.0
    for object in bpy.context.selected_objects:
        interval += step
        if object.animation_data !=  None:
            fcurves = object.animation_data.action.fcurves
            for curve in fcurves:
                keyframepoints = curve.keyframe_points
                for point in keyframepoints:
                    point.co.x += interval 
                    point.handle_left.x += interval
                    point.handle_right.x += interval
                    
                
shift(10)


The script will loop through the fcurves of the selected objects and will increment the x value of each point.
Caveat:

the script doesn't allow to set the order of the objects.
the script will shift ALL the keyframes